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Maksim231197 [3]
3 years ago
12

What is the volume of this solid? A. 1104 B. 132 C. 96 D. 276

Mathematics
1 answer:
statuscvo [17]3 years ago
6 0

For this case we have that the volume of the figure is composed of the volume of a prism and the volume of a pyramid:

The volume of the prism is given by:

V = A_ {b} * h

Where:

A_ {b}: It is the area of the base

h: It's the height

Substituting:V = 6 * 6 * 6\\V = 216 \ units ^ 3

The volume of the pyramid is given by:

V = \frac {1} {3} * L ^ 2 * h

Where:

L ^ 2:It is the area of the base

h: It's the height

Substituting:

V = \frac {1} {3} * 6 ^ 2 * 5\\V = \frac {1} {3} * 36 * 5\\V = 60units ^ 3

We add and we have:

V = 276 \ units ^ 3

ANswer:

Option D

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The plans for a new ammusement park were laid out on the first quadrant of a coordinate plane. The entrance to the roller coaste
Solnce55 [7]

The first step is to determine the distance between the points, (1,1) and (7,9)

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\begin{gathered} \text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ \text{From the graph, } \\ x1\text{ = 1, y1 = 1} \\ x2\text{ = 7, y2 = 9} \\ \text{Distance = }\sqrt[]{(7-1)^2+(9-1)^2} \\ \text{Distance = }\sqrt[]{6^2+8^2}\text{ = }\sqrt[]{100} \\ \text{Distance = 10} \end{gathered}

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4 0
1 year ago
Solve for x: 3/3x + 1/x+4 = 10/7x
Mekhanik [1.2K]
Given,

3/3x + 1/(x + 4) = 10/7x

1/x + 1/(x+4) = 10/7x

Because the first term on LHS has 'x' in the denominator and the second term in the LHS has '(x + 4)' in the denominator. So to get a common denominator, multiply and divide the first term with '(x + 4)' and the second term with 'x' as shown below

{(1/x)(x + 4)/(x + 4)} + {(1/(x + 4))(x/x)} = 10/7x

{(1(x + 4))/(x(x + 4))} + {(1x)/(x(x + 4))} = 10/7x

Now the common denominator for both terms is (x(x + 4)); so combining the numerators, we get,

{1(x + 4) + 1x} / {x(x + 4)} = 10/7x

(x + 4 + 1x) / (x(x + 4)) = 10/7x

(2x + 4) / (x(x + 4)) = 10/7x

In order to have the same denominator for both LHS and RHS, multiply and divide the LHS by '7' and the RHS by '(x + 4)'

{(2x+4) / (x(x + 4))} (7 / 7) = (10 / 7x) {(x + 4) / (x + 4)}

(14x + 28) / (7x(x + 4)) = (10x + 40) / (7x(x + 4))

Now both LHS and RHS have the same denominator. These can be cancelled. 

∴14x + 28 = 10x + 40
14x - 10x = 40 - 28
4x = 12
x = 12/4

∴x = 3



8 0
3 years ago
Write each mixed number as m/n in simplest form where m/n are integers 7 7/9
Svetach [21]
70/9

7 is equivalent 63/9, and then you add 63 and 7 to get 70/9
6 0
3 years ago
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